BibTeX
@ARTICLE{
Bischof2004TPC,
author = "C. H. Bischof and H. M. B{\"u}cker and P.T. Wu",
title = "TimeParallel Computation of PseudoAdjoints for a Leapfrog Scheme",
journal = "International Journal of High Speed Computing",
pages = "127",
doi = "doi:10.1142/S0129053304000219",
abstract = "The leapfrog scheme is a commonly used secondorder difference scheme for solving
differential equations. If~$Z(t)$ denotes the state of a system at a particular time step~$t$, the
leapfrog scheme computes the state at the next time step as~$Z({t+1}) = H(Z(t), Z({t1}), W)$,
where~$H$ is the nonlinear timestepping operator and~$W$ represents parameters that are not
timedependent. In this note, we show how the associativity of the chain rule of differential
calculus can be used to compute a socalled adjoint, the derivative of a scalarvalued function
applied to the final state~$Z(T)$ with respect to some chosen parameters, efficiently in a parallel
fashion. To this end, we (1)~employ the reverse mode of automatic differentiation at the outermost
level, (2)~use a sparsityexploiting version of the forward mode of automatic differentiation to
compute derivatives of~$H$ at every time step, and (3)~exploit chain rule associativity to compute
derivatives at individual time steps in parallel. We report on experimental results with a 2D
shallow water equations model problem on an IBM~SP parallel computer and a network of Sun
SPARCstations.",
ad_area = "Oceanography",
ad_tools = "Adifor",
ad_theotech = "Sparsity",
year = "2004",
volume = "12",
number = "1"
}
